The categories $L$\textbf{-Top_0} and $L$$\mathbf{\text{Sob}}$ as epireflective hulls

We show that the category $L{\mathbf{\text{-Top}}}_0$ of $T_0$-$L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L\mathbf{\text{-Top}}$ of $L$-topological spaces and the category $L\mathbf{\text{-Sob}}$ of sober $L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L{\mathbf{\text{-Top}}}_0$.